My parents wouldn't let me cut my hair until I was 8. So, when I was 8, I cut it about as short as OP's DD. I liked it for a bit, then hated it. BUT, at least I was given the opportunity. I would probably have my DD wait until she was just a bit older. Even when I wanted short hair at 5 or 6, at least I knew that once I reached an age I would be able to cut it instead of being flat out told no.

seeing as during my senior year i had mine cut very similarly (went from hair so long i could sit on it, to that short) i would let my dd if she wanted. i might try to convince her to shorten it a little and then we could cut more if she still wanted, just so she wouldn't be devastated like i was lol.
mine was more out of frustration than wanting it short. i was on the fire dept and we'd had a tornado come through. i had been up on a roof with a chainsaw cutting a tree that fell through someone's roof, and my hair kept coming out from under my helmet and into my face. when i got home i told my mom that either she could cut it super short or i would shave it. knowing my impulsiveness, she cut it so i wouldn't actually shave my head lol. i called her thenext day crying because i was so upset ...not at her, but because i loved my long hair.